David Allen Hoffman

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David Allen Hoffman (born July 21, 1944 in Far Rockaway , Queens , New York ) is an American mathematician who deals with differential geometry and especially minimal surfaces .

Hoffman studied at the University of Rochester (Bachelor's degree in 1966) and at Stanford University , where he made his master's degree in 1969 and received his doctorate in 1971 with Robert Osserman ( Surfaces in Constant Curvature Manifolds with Parallel Mean Curvature Vector Field ). In 1972 he was a lecturer at the University of Durham , 1972/73 Assistant Professor at the University of Michigan and from 1974 Assistant Professor and later Professor at the University of Massachusetts Amherst (UMass). Since 1994 he has headed the Scientific Graphics Project of UMass and MSRI . Among other things, he was visiting professor at the University of Paris VII (1989), at the Institute for Pure and Applied Mathematics in Rio de Janeiro (1981) and at Stanford University (1978). He is a fellow of the American Mathematical Society .

He is concerned with the geometry of immersed submanifolds including minimal areas, variation inequalities and isoperimetric inequalities in Riemannian geometry , computer graphics methods in mathematics and the application of variation methods to the microstructure of composite polymer materials.

In particular, he is known for the construction of new ( embedded ) minimal surfaces from the 1980s. Then the field of minimal surfaces received a boost after the surprising discovery of a new full , embeddable minimal surface in three-dimensional Euclidean space without self-intersection by the Brazilian mathematician Celso José da Costa in 1982 in his dissertation - previously thought to the level that catenoid and the helicoid would be the single examples. Hoffman found in 1984 with the help of computers with William Meeks III (also professor at UMass) Costas example, starting a whole class of new such minimal surfaces, where they also with the programmer Jim Hoffman worked together (James T. Hoffman). The surface had an infinite topological gender. He also worked with Hermann Karcher when they found entire families of such areas with finite topological gender, but the evidence for the case genus 1 was not provided until 2009 by Hoffman, Matthias Weber and Michael Wolf .

In 1990 he received the Chauvenet Prize for The Computer-Aided Discovery of New Embedded Minimal Surfaces .

Fonts

  • Editor Global Theory of Minimal Surfaces , Proc. Clay Math. Institute 2001, American Mathematical Society, Clay Mathematics Institute 2005
  • with MJ Callahan, Jim Hoffman Computer graphics tools for the study of minimal surfaces , Communications of the ACM, Volume 31, 1988, pp. 648-661.
  • Hoffman, Meeks A complete embedded minimal surface in R3 with Genus 1 and three ends , J. Diff. Geom., Vol. 21, 1985, pp. 109-127.
  • with Hermann Karcher Complete embedded minimal surfaces of finite total curvature , in Robert Osserman (editor) Geometry V , Encyclopedia of Mathematical Sciences, Volume 90, Springer Verlag 1997
  • with M. Weber, M. Wolf: An embedded genus-one helicoid , Annals of Mathematics, Volume 169, 2009, pp. 347-448 (and Proc. Nat. Acad. USA, Volume 102, 2005, pp. 16566-16568 )

Web links

Individual evidence

  1. ↑ Life and career data according to American Men and Women of Science , Thomson Gale 2005
  2. ↑ David Allen Hoffman in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used Template: MathGenealogyProject / Maintenance / name used
  3. ↑ Especially without a margin
  4. ↑ Costa minimal area at Mathworld
  5. ↑ Later known primarily for his conspiracy theories on the World Trade Center assassination attempt in 2001
  6. ^ Mathematical Intelligencer. Volume 9, 1987, pp. 8-21
personal data
SURNAME Hoffman, David Allen
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH July 21, 1944
PLACE OF BIRTH Far Rockaway